Fig. 2: Computation of logarithm of P-peak of displacement vs. time (LPDT) curves and slope measurement.
From: The deterministic behaviour of earthquake rupture beginning
A Color represents two different magnitude values (cyan is Mw = 4, red is Mw = 7). Dotted lines show the LPDT curves at each station; thick lines show the averaged LPDT curve. The circle (corresponding to tMIN = 0.05 s) is the starting point for the slope evaluation. The diamond (tHALF) is the ending point for slope evaluation, corresponding to half-time of the maximum LPDT curvature. Slope is evaluated as \(({{\rm{L}}}{{\rm{P}}}{{\rm{D}}}{{\rm{T}}}({{t}}_{{{\rm{H}}}{{\rm{A}}}{{\rm{L}}}{{\rm{F}}}})-{{\rm{L}}}{{\rm{P}}}{{\rm{D}}}{{\rm{T}}}({{t}}_{{{\rm{M}}}{{\rm{I}}}{{\rm{N}}}}))/({{t}}_{{{\rm{H}}}{{\rm{A}}}{{\rm{L}}}{{\rm{F}}}}-{{t}}_{{{\rm{M}}}{{\rm{I}}}{{\rm{N}}}})\). The figure inset shows a sketch of station selection for LPDT curves evaluation: only the records between the closest station to the event epicenter (yellow star) falling within a circular crown of 25 km are taken into account. B shows an example of the averaged LPDT curve for each magnitude bin. To appreciate initial slope variation, the curves are shifted to their initial point LPDT0. C shows the LPDT curvatures of LPDT in (B). The maximum curvature is reached at the plateau level of each LPDT curve.
